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The definition of the absolute value for a fuzzy number is obtained.Furthermore,a lot ofproblems,such as absolute integrability,bounded variation and absolute continuity,arepresented and discussed.The representation theorem of the absolute values of fuzzy num-bers is established.It plays an important role in discussing the problems conceming theabsolute value.The relation between the absolute integrability and integrabili-ty is discussed,and the following result is obtained:aintegrable fuzzy-number-valued function is absolutely integrable iff it is integrable.The relation between theabsolute integrability and the absolute continuity of the primitive for fuzzy-number-valuedfunctions is dealt with.It is also pointed out that a fuzzy number valued function is ab-solutelyintegrable if and only if its integral primitive is fuzzy absolutely continuous.

提出了模糊数绝对值的概念并讨论了与绝对值相关的一系列问题，如绝对可积性、有界变差性、绝对连续性等，给出了模糊数绝对值的定义以及表示定理，该表示定理在涉及绝对值问题的讨论中起非常重要的作用；讨论了绝对可积与可积之间的关系，得到了结论：可积的模糊数值函数绝对可积的充要条件是该模糊数值函数可积；给出了模糊数值函数绝对可积与其积分原函数绝对连续性之间的关系，指出模糊数值函数绝对可积的充要条件是其原函数模糊绝对连续。

On this basis from the fuzzy set with the classic set of relations, the application of fuzzy set of the latest set of decomposition theorem, A new fuzzy definition of the fuzzy distance, definition and application of this research is partial order triangular fuzzy numbers fuzzy distance.

在此基础上从模糊集与经典集的关系出发，应用模糊集的截集以及分解定理，提出一种新的模糊集的模糊距离定义，并应用此定义研究具有偏序关系的三角模糊数的模糊距离。

In this thesis, we defined duality Fuzzy relation in a pointwise Fuzzy set by a set of duality Fuzzy point. Then we defined Fuzzy congruence and Fuzzy rough set in Fuzzy semigroups.

本文把二维模糊点作成的集合定义为一个点态化模糊集上的模糊二元关系，进一步定义模糊同余关系，并通过它又定义点态化模糊集上模糊粗糙子集，并研究了它们的一些性质。

In the sense of cutset, the relation between the rough set of a cutset and the cutset of a rough set, a fuzzy rough set of a fuzzy primary ideal in a semigroup is proved to be its fuzzy primary ideal. The sixed chapter is Rough Primary Ideals and Rough Fuzzy Primary Ideals in rings, the corresponding results of a semigroup are generalized in a ring. The last chapter is Rough-fuzzy Subsemirings in Semirings, First, the lower and upper rough-fuzzy semirings together with the left and the right ideal are defined.

利用截集意义下，截集的粗糙集与粗糙集截集的关系，证明了在完备同余关系下半群中的模糊准素理想的粗糙集是模糊准素理想；第六章是环中粗准素理想和粗模糊准素理想，将半群中的相(来源：A70BC论文网www.abclunwen.com)应结果推广到环中；第七章是半环中的粗模糊子半环，首先，给出上粗模糊子半环及上粗模糊理想等概念，并研究了它们的性质。

In order to embody the fuzzy character in evaluation, the traditional analytic hierarchy process is developed into a fuzzy one. The introduction of triangular fuzzy number can contain more fuzzy information of evaluation. The ranking method for reciprocal judgement matrix with triangular fuzzy numbers is also presented. Based on the mode identification process, the mathematical model of multi-level and multi-object evaluation using fuzzy approach degree is set up primarily.

为了更加有效地反映评估对象的模糊性，本研究将传统的层次分析法拓展到模糊领域，引入三角模糊数的概念，并对模糊评判矩阵的排序方法进行了研究，在此基础上，提出了基于模糊集贴进度的模式识别评估方法，建立起润扬大桥悬索桥多层次多目标综合评估模型。

Around the finite solution problem of fuzzy differential equation, the fuzzy structure element method is put forward about the calculation of fuzzy analysis, and this method is applied to systematically study many problems such as formulation of fuzzy-valued function, difference of fuzzy-valued function, integration of fuzzy-valued function under the Riemann meaning, and the solution structure of fuzzy differential equation etc..

围绕模糊微分方程定解问题，提出了模糊分析计算的模糊结构元方法，并利用模糊结构元的方法对模糊值函数的表述问题、模糊值函数的微分、黎曼意义下的模糊值函数积分以及模糊微分方程的解的结构等问题，进行了深入系统的研究。

In this paper,fuzzy complex numbers,limits of the sequence of fuzzy complex numbers,the metrical convergence and levelwise convergence,the continuity offuzzy complex functions,the calculus of fuzzy complex functions,theseries whose terms are fuzzy complex numbers,the series whose terms arefuzzy complex functions,the fuzzy complex measure and fuzzy differentialequation are investigated in details.All this may be a foundation forfurther researching fuzzy complex analysis.

本文对模糊复数、模糊复数列的极限、度量收敛与水平收敛、模糊复函数的连续性、模糊复函数的微积分、模糊复数项级数、模糊复函数项级数、模糊复测度及模糊微分方程理论进行了详细的研究，为模糊复分析的进一步研究打下一定基础。

of transitive closure based on equivalence relation, method of maximum fuzzy spanning tree based on fuzzy graph, and algorithm Fuzzy C-Means based on partition are more deeply investigated. Respectively, this thesis proposes an algorithm for document fuzzy clustering based on methed of transitive closure and an algorithm for document fuzzy clustering based on methed of maximum fuzzy spanning tree. Moreover, FCM is particularly studied from data standardization method, metrics method, and selection method of initial clustering prototype.

较深入地讨论了基于等价关系的传递闭包法、基于模糊图论的最大树法以及基于划分的模糊C-均值算法，分别提出了基于传递闭包法的文本模糊聚类方法ATCFC和基于最大树法的文本模糊聚类方法ATCMT；重点从改变规格化方式、改变度量方式、改变初始聚类原型选择方式三方面对FCM算法进行研究。

In accordance with the technological difficulties encountered in the process of insulation supervision based on the Dissolved Gases Analysis,several kinds of model and method are presented to improve the reliability and precision of fault diagnosis of the power transformer. Main research content includes:By deeply studying the common transformer faults diagnosing methods,such as three-ratio methods and improved electrical committee agreements,several shortcomings such as uncertainness judgment when the fault reasons,phenomenon and principles come out together while can not consistent to each other etc. For this reason,the old methods can not fully meet the need to engineering practical application.Considering fuzzy relationship matrix can fully represents the causality between fault symptoms and fault types,when diagnosing complex equipments with multiple symptoms and fault causes such as power transformer,a synthetic fuzzy diagnosing model is firstly proposed to diagnose transformers insulation faults based on DGA in this paper. Meanwhile,by further study the character of fuzzy factors,aimed at correcting the defects in classifying fuzzy sets of common fuzzy judgment,a method are put forward by unifying fuzzy synthetic diagnosis and fuzzy principle reasoning.

本文针对应用油中溶解气体分析方法进行变压器绝缘监督时所遇到的主要技术难点，提出了提高变压器故障诊断的准确性、可靠性的几种模诊断方法，主要研究内容有：通过对判断变压器故障常用的三比值法和改良电协研法的深入分析，其诊断准确率较高，但对故障原因、故障现象和故障机理间同时存在不确定性和模糊性的变压器等电气设备的故障诊断，难于满足工程应用的需要；在处理变压器等结构复杂设备的多症状、多原因故障诊断时，模糊关系矩阵可以全面反映这种症状与故障类型间的因果关系，进而提出了变压器故障诊断的模糊综合诊断模型；同时作者还深入分析了模糊算子的特性；针对常用的模糊评判结果的模糊集的集化方法的不足性，提出了将模糊综合诊断与模糊规则推理结合起来进行故障诊断的方法，能达到较好的效果。

Engrafting L.A.Zadeh one branch fuzzy decision theory with RSA algorithm in information security, this paper gives concepts of multi-cooperation encryption and multi-cooperation sharing fuzzy decision; innovatively gives mathematical structures of group encryption and multi-group sharing fuzzy decision; finally gives safe fuzzy decision algorithm and its applications; safe fuzzy decision is a new direction of fuzzy decision research.

将L.A.Zadeh单枝模糊决策理论与信息安全中的RSA算法相互嫁接，相互渗透，提出了多合作加密与多合作共享模糊决策的概念；创新性地给出了集团加密与多集团共享模糊决策的数学结构；最后给出安全模糊决策算法以及它的应用；安全模糊决策是模糊决策研究的一个新的方向。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失